Nakayama automorphism and applications
Nakayama automorphism is used to study group actions and Hopf algebra actions on Artin-Schelter regular algebras of global dimension three.
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arXiv subjects
Jiafeng Lu
Publications and source records attributed to Jiafeng Lu.
On an example of δ-Koszul algebras
The main purpose of this paper is to study a concrete example of $δ$-Koszul algebras, which is related to three questions raised by Green and Marcos in [3].
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Piecewise-Koszul algebras
It is a small step toward the Koszul-type algebras. The piecewise-Koszul algebras are, in general, a new class of quadratic algebras but not the classical Koszul ones, simultaneously they agree with both the classical Koszul and higher Koszul algebras in special cases. We give a criteria theorem for a graded algebra $A$ to be piecewise-Koszul in terms of its Yoneda-Ext algebra $E(A)$, and show an $A_{\infty}$-structure on $E(A)$. Relations between Koszul algebras and piecewise-Koszul algebras are discussed. In particular, our results are related to the third question of Green-Marcos' [6].
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Quasi-Koszulity and minimal Horseshoe Lemma
In this paper, the criteria for minimal Horseshoe Lemma to be true are given via quasi-$δ$-Koszul modules, which are the nongraded version of $δ$-Koszul modules first introduced by Green and Marcos in 2005. Moreover, some applications of minimal Horseshoe Lemma are also given.
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